While interviewing in the U.S. you'll get a lot of casual questions about your current job, such as what you like best about it, what skills you use there or why you want to leave. These will come from the recruiter, the manager and your future peers. These are both technical and social questions. Refusing to answer any of these questions would be very weird socially, and even very restrictive NDAs should allow you to at least speak generally about what you're doing.
>"While interviewing in the U.S. you'll get a lot of casual questions about your current job, such as what you like best about it, what skills you use there or why you want to leave. "
These fall perfectly into experience with last job. Does not have to be current. And all those questions you asked are trivial. Also I've never dealt with the recruiters. I have always searched and found perspective companies myself and no they were not Amazon big type. If I could not speak with the owner I would simply walk away - not my kind of place.
My first programming job in Canada - I just simply walked into the office and asked to speak to the owner (I knew it was small 20 person consultancy).
Since 2000 I am on my own but I still find clients and have interviews. Just a different type of interview of course.